Abstract
Vibration problems of a segment of winding between two clamping plates are studied when the clamping plates, which are used to fix stator end winding, are loose. First, magnetic induction expressions of the winding while the generator was running were given by using separation of variables method. Also, the expressions of the winding electromagnetic force and dry friction force between loosing clamping plates were gotten. Secondly, a mechanical model, which was used to study nonlinear vibration problem of the winding, was set up. Fundamental resonance was analyzed by using multiple scales method, and a resonance equation of amplitude and frequency in steady state was given. Then stability, bifurcation and singularity of the steady solution were studied. Criterions of stability and transition set of the bifurcation equation were obtained. At last, through numerical calculations, resonance curves were obtained. The results are helpful for analysis and protection of generator accidents.
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References
Qiu Jiajun. Nonlinear vibration study of coupled mechanical and electric and coupled magnetic and solid of generators[J].Proceedings of the Chinese Society for Electrical Engineering, 2002,22(5): 109–115 (in Chinese).
Wang Geng, Wang Zuomin, Shao Yasheng,et al. Vibration problem in turbo-generators(I)[J].Journal of Vibration and Shock, 1999,18(4): 1–5 (in Chinese).
Hu Yuda. Study of vibration problem of a large-scale turbo-generator stator end winding excited by electromagnetic force[D]. Ph D dissertation. Tianjin University, Tianjin, 2003, 12–14 (in Chinese).
Tang Yunqiu.Electromagnetic Field in Motor[M]. Science Press, Beijing, 1981, 278–306 (in Chinese).
Wollegack A E. The fundamental method of calculation of the magnetic field in generator end winding[J].Electricity, 1963, (1): 42–48 (in Chinese).
Ambarcumian S A, Bagdasarian G E, Belubekian M V.Magneto-Elastic of Think Shell and Plat [M]. Science, Moscow, 1997, 150–163 (in Chinese).
Wickert J A. Analysis of self-excited longitudinal vibration of a moving tape[J].Journal of Sound and Vibration, 1993,160(3): 455–463.
Stelter P. Nonlinear vibrations of structures induced by dry friction[J].Nonlinear Dynamics, 1992,3(3): 329–345.
Nayfeh A H, Mook D T.Nonlinear Oscillations[M]. John Wiley & Sons, New York, 1979, 203–219.
Golubisky M, Schaefler D G.Singularities and Groups in Bifurcation Theory[M]. Springer-Verlag, New York, 1985, 267–271.
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Communicated by Li Li, Original Member of Editorial Committee, AMM
Project supported by the National Natural Science Foundation of China (No. 10072038) and the Doctoral Foundation of Education Ministry of China (No. 2000005616)
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Yu-da, H., Jia-jun, Q. & Na, T. Fundamental resonance and bifurcation of large generator end winding when its clamping plates are loose. Appl Math Mech 26, 505–514 (2005). https://doi.org/10.1007/BF02465390
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DOI: https://doi.org/10.1007/BF02465390